Time taken by pipe A and pipe B to fill up the cistern is 12 minutes whereas time taken by pipe C to empty the whole cistern is twice that of time taken by A and B together to fill the tank and ratio of time taken by pipe A and B to fill up the tank when operating alone is 2 : 3. If pipe A and B are alternatively opened every 6 minutes and C is opened with pipe B but closed when pipe A is opened then calculate total time taken to fill up the whole cistern.